Optimal life-cycle capital taxation under self-control problems

We study optimal taxation of savings in an economy where agents face self-control problems, and we allow the severity of self-control to change over the life cycle. We focus on quasi-hyperbolic discounting with constant elasticity of inter-temporal substitution utility functions and linear Markov equilibria. We derive explicit formulas for optimal taxes that implement the efficient (commitment) allocation. We show, analytically, that if agents’ ability to self-control increases concavely with age, then savings should be subsidised and the subsidy should decrease with age. We also study the quantitative effects of age-dependent self-control problems and find that the optimal subsidies in our environment are much larger than those implied by models with constant self-control. Finally, we compare our optimal subsidies with those implied by the 401(k) plan. Although the subsidy levels in the two cases are of comparable magnitudes, the 401(k) plan implies an increasing pattern of subsidies while the optimal subsidies decrease over the life cycle.